[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

If n is even ...

Posted By: Nack Ballard
Date: Sunday, 16 May 2010, at 5:15 p.m.

In Response To: If n is even ... (Bob Koca)

Regarding sudoku, I haven't seen the discussions to which you refer, but the external/internal symmetries and line-shuffling ideas had occurred to me independently, and I've often wondered if sudoku books simply take the same basic puzzle(s) and rotate, reflect and shuffle them into different variants. (Chances are it happens inadvertently, at least.)

You're right that the same line-shuffle ideas can be applied to the even-numbered tic-tac-X grids; I hadn't thought of that.

For example with a 3 by 3 grid with 4 spaces filled in, instead of 9C4 = 126 positions I see only 4:

1) (1,1) (1,2) (2,1) (2,2)
2) (1,1) (1,2) (2,1) (2,3)
3) (1,1) (1,2) (2,1) (3,3)
4) (1,1) (1,2) (2,3) (3,3)

Your example employs an odd-N grid here, though I'm less sure of your transpositional methodology. Forgive my translating your code to algebraic; it's a lot less typing and I find it less confusing:

(1) a1 a2 b1 b2
(2) a1 a2 b1 b3
(3) a1 a2 b1 c3
(4) a1 a2 b3 c3

You seem to imply (for example) that a1 b1 b2 c2 is the same as (2) above, because columns b and c can freely be switched and rows 1 and 2 can be switched at the same time (followed by the appropriate rotation/flip) without materially affecting the play with non-diagonal rules. Is that what you mean?

Nack

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.